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Stefan-Boltzmann radiation on nonconvex surfaces. (English) Zbl 0872.35044
The paper contains some results concerning the existence of a solution for the stationary heat equation in a non-convex body with Stefan-Bolzmann radiation condition on the surface. The author derives the equations for the heat balance on the radiating surface. Then the stationary heat equation with nonlocal radiation boundary condition is formulated. The problem is nonlinear and in the general case non-coercive. The purpose of the paper is to prove the existence and uniqueness of a weak solution. The proof of the main result makes use of the existence of super- and subsolutions. Finally, some special cases are also discussed with stronger existence results.

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
80A20 Heat and mass transfer, heat flow (MSC2010)
35B50 Maximum principles in context of PDEs
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References:
[1] Delfour, SIAM J. Numer. Anal. 24 pp 1077– (1987)
[2] and , Fundamentals of Heat and Mass Transfer, Wiley, Chichester, 1985.
[3] Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris, 1969.
[4] Multidimensional Singular Integrals and Integrals Operators, Pergamon, Oxford, 1965.
[5] and , Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967.
[6] Banach Lattices and Positive Operators, Springer, Berlin, 1974. · Zbl 0296.47023
[7] Nonlinear Functinal Analysis II B, Nonlinear Monotone Operators, Springer, Berlin, 1988.
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